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  <title>Four Reaction Wheels</title>
                                         
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<div align="center"> <img src="RW%20Control.GIF" alt="RW Control"
 width="207" height="46">
<b><u><br>
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<div align="left"><b><u>Description<br>
 </u></b><br>
   An attitude maneuver via momentum transfer based on the conservation of<br>
   angular momentum was simulated. In this project, 4 reaction wheels in
<br>
   a pyramid configuration was used; this configuration provides redundancy 
 <br>
   such that if one wheels become unable to operate for some reason, <br>
   the other three reaction wheels can provide control torque in all three
 direction. <br>
   <br>
   <img src="FourReactionWheel.GIF"
 alt="Four Reaction wheels in a pyramid configuration" width="541"
 height="399">
   <br>
         <br>
   <b><u>Inputs<br>
 </u></b><br>
      <b>Ixx</b>,<b> Iyy, Izz</b>                &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; Moments of inertia<br>
      <b>J</b>                               &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160;
Reaction wheel inertia<br>
   <b>  RW angle&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;</b>                  Tilt angle of reaction
wheel axis<br>
   <b>  psi</b>                             &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; Commanded 
Euler angle<br>
   <b>  phi  </b>&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;                          Commanded 
Euler angle<br>
   <b>  theta</b>                         &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; Commanded Euler 
angle<br>
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     <b><u>Initial Condition</u></b><br>
   <b>w1</b>, <b>w2, w3</b>:                 &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; Spacecraft angular 
velocities <br>
         <b>q1, q2, q3, q4</b>:            &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; Quaternions<br>
    <b>Omega1 </b>&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;                     Angular velocity 
of RW 1<br>
   <b>  Omega2</b>                      &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; Angular velocity 
of RW 2<br>
   <b>  Omega3 </b>&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;                     Angular velocity 
of RW 3<br>
   <b>  Omega4</b>                      &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; &#160;&#160;&#160; Angular velocity 
of RW 4<br>
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